Maximum Likelihood Estimation of Optical Path Length in Spectral Interferometry

Optical path length demodulation is a subject of fundamental importance in spectral interferometry applications. We propose an algorithm based on maximum likelihood estimation to achieve absolute optical path length demodulation with high sensitivity and noise resistance and to elucidate the cause and behavior of undesirable demodulation discontinuity. From an interference spectrum model with additive Gaussian noise, a maximum likelihood estimator is derived in Fourier domain to determine the optical path length. To assess its sensitivity performance, the Cramer-Rao bound of sensitivity is derived from Fisher information matrix. By simulations and experimental validations, the proposed method demonstrates its capability of achieving the Cramer-Rao bound over a large dynamic range of optical path lengths, initial phases, and signal-to-noise ratios. When compared with some state-of-the-art demodulation methods, it also demonstrates improved resistance to demodulation jumps at low signal-to-noise ratios. Importantly, the mechanism of such jumps can be readily explained from a new, intuitive perspective, which may permit the quantification of jump occurrences in the future.